I've got much the same problem, but not just with h.264.
I edited the movie in FCP and graded in Color, using a Panasonic 1710 through a Blackmagic 3D Extreme card. My computer monitor is the basic Apple 27". Final use of the project will be for projection, but I need to show it first on computer monitors. The colors I'm seeing in FCP on the Apple monitor are about the same as on the Panasonic, just darker overall because of the difference in gamma.
First I exported a version for Vimeo via Compressor, as an h.264 mp4 Quicktime. I noticed that the colors were more desaturated than what I was seeing on my computer monitor. I assumed this was because of the h.264 compression, so did a straight Quicktime output from FCP (File::Export::Quicktime Movie...) to compare. Both exports looked the same in terms of color and gamma, though the QT movie is 422HQ.
Here is a screen shot of the three outputs (can't include the broadcast monitor, of course)
So I'm baffled as to the color/saturation difference, and can find nothing in the settings to help. Any ideas?
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